In reference to footnote 2, Eddington came up with a great idea for measuring lifetime accomplishments:

Eddington number for cycling

Eddington is credited with devising a measure of a cyclist's long-distance riding achievements. The Eddington number in the context of cycling is defined as E, the number of days a cyclist has cycled more than E miles. For example an Eddington number of 70 would imply that a cyclist has cycled more than 70 miles in a day on 70 occasions. Achieving a high Eddington number is difficult since moving from, say, 70 to 75 will probably require more than five new long distance rides since any rides shorter than 75 miles will no longer be included in the reckoning. Eddington's own E-number was 84. /end description

I think we should use Eddington numbers for all kinds of stuff:

One alternate use of an Eddington number could be number of years E where you donated more than E% of your income to charity.

There could also be situations where a low Eddington number is a good sign. For instance, number of weeks E where you watched at least E hours of television.

I'm not convinced that Randall's analysis is complete. The tidal forces work both ways and the moon has a tidal bulge. The swap to a black hole will alter this interaction and will ultimately have an effect on the Earth.

sjm27 wrote:I'm not convinced that Randall's analysis is complete. The tidal forces work both ways and the moon has a tidal bulge. The swap to a black hole will alter this interaction and will ultimately have an effect on the Earth.

Earth's gravity presently produces a 51 cm tidal bulge in the moon, but that is not enough to have any feedback effect on Earth. All other interactions will remain the same.

I'm actually more interested in his answer to the eclipse question. Seems like there should be noticeably significant gravitational lensing during an eclipse event...perhaps resulting in a laser-like solar beam carving a smoking path across Earth's surface. Unfortunately my relativity-fu and optics-fu are not good enough to work in combination to figure out the likelihood of this.

sjm27 wrote:I'm not convinced that Randall's analysis is complete. The tidal forces work both ways and the moon has a tidal bulge. The swap to a black hole will alter this interaction and will ultimately have an effect on the Earth.

Earth's gravity presently produces a 51 cm tidal bulge in the moon, but that is not enough to have any feedback effect on Earth. All other interactions will remain the same.

I'm actually more interested in his answer to the eclipse question. Seems like there should be noticeably significant gravitational lensing during an eclipse event...perhaps resulting in a laser-like solar beam carving a smoking path across Earth's surface. Unfortunately my relativity-fu and optics-fu are not good enough to work in combination to figure out the likelihood of this.

The gravitational lensing effect of a lunar-mass black hole orbiting at a distance of approx 1.3 light-seconds above the earth would be the about same as a the lensing effect of a proton-mass black hole directly in front of you at about arm's length.

sevenperforce wrote:I'm actually more interested in his answer to the eclipse question. Seems like there should be noticeably significant gravitational lensing during an eclipse event...perhaps resulting in a laser-like solar beam carving a smoking path across Earth's surface. Unfortunately my relativity-fu and optics-fu are not good enough to work in combination to figure out the likelihood of this.

The gravitational lensing effect of a lunar-mass black hole orbiting at a distance of approx 1.3 light-seconds above the earth would be the about same as a the lensing effect of a proton-mass black hole directly in front of you at about arm's length.

But there would be one interesting effect: In addition to getting darker, Earth would get colder, because moonlight warms the Earth. It's a very tiny contributor to our global energy balance; the Moon is five or six orders of magnitude dimmer than the Sun. But it's there.

This is not true. The earth would get warmer, because the main contribution of the moon to the global energy balance are solar eclipses, as seen on top of the What-If post. The moon blocks the sunlight for hours approximately two times the year. An effect, that should be in the order of magnitude of nearly 0.1% of the total sunlight.

But there would be one interesting effect: In addition to getting darker, Earth would get colder, because moonlight warms the Earth. It's a very tiny contributor to our global energy balance; the Moon is five or six orders of magnitude dimmer than the Sun. But it's there.

This is not true. The earth would get warmer, because the main contribution of the moon to the global energy balance are solar eclipses, as seen on top of the What-If post. The moon blocks the sunlight for hours approximately two times the year. An effect, that should be in the order of magnitude of nearly 0.1% of the total sunlight.

Can you correct this?

Best regards,Uli2

Lunar eclipses only cover a small portion of the earth's surface, so I think it's a lot smaller effect than that. Interesting point, though.

sevenperforce wrote:I'm actually more interested in his answer to the eclipse question. Seems like there should be noticeably significant gravitational lensing during an eclipse event...perhaps resulting in a laser-like solar beam carving a smoking path across Earth's surface. Unfortunately my relativity-fu and optics-fu are not good enough to work in combination to figure out the likelihood of this.

The gravitational lensing effect of a lunar-mass black hole orbiting at a distance of approx 1.3 light-seconds above the earth would be the about same as a the lensing effect of a proton-mass black hole directly in front of you at about arm's length.

So it has to do with the angular area?

The distortion effect has a lot to do with angular area. The only light beams that would be lensed are those that are tangent or nearly tangent to the EH of the black hole. Because the number of photons that hits your eye is inversely proportional to the square of the distance of the object you are looking at (and directly proportional to its apparent size), the closer you are to the object, the smaller it has to be to give the same optical effect. To put it another way, how much lensing do you see if you looked at the galactic core? A lunar-mass moon would have roughly the same amount.

sjm27 wrote:I'm not convinced that Randall's analysis is complete. The tidal forces work both ways and the moon has a tidal bulge. The swap to a black hole will alter this interaction and will ultimately have an effect on the Earth.

Earth's gravity presently produces a 51 cm tidal bulge in the moon, but that is not enough to have any feedback effect on Earth. All other interactions will remain the same.

I'm actually more interested in his answer to the eclipse question. Seems like there should be noticeably significant gravitational lensing during an eclipse event...perhaps resulting in a laser-like solar beam carving a smoking path across Earth's surface. Unfortunately my relativity-fu and optics-fu are not good enough to work in combination to figure out the likelihood of this.

The gravitational lensing effect of a lunar-mass black hole orbiting at a distance of approx 1.3 light-seconds above the earth would be the about same as a the lensing effect of a proton-mass black hole directly in front of you at about arm's length.

And? How much is that? I don't have a proton-sized black hole nearby to see for myself...

I had that song stuck in my head whole day for some reason, finally managed to get rid of it, and then I open this what if. My sleep-deprived brain actually thought it was some kind of prank for a couple of seconds.

Uli2 wrote:The earth would get warmer, because the main contribution of the moon to the global energy balance are solar eclipses, as seen on top of the What-If post. The moon blocks the sunlight for hours approximately two times the year. An effect, that should be in the order of magnitude of nearly 0.1% of the total sunlight.

Lunar eclipses only cover a small portion of the earth's surface, so I think it's a lot smaller effect than that. Interesting point, though.

Typically, the totality track of the moon's shadow during an eclipse is approximately 250 km wide. The maximum duration of an eclipse is a little over two hours. While totality does not exist for this entire duration, we will pretend it does for the purposes of establishing an upper bound.

With the above values, each eclipse blocks a 4.9e10 m2 of area for two hours. Solar insolation at the top of the atmosphere is 1.37 kW/m2, so each eclipse blocks a total of 4.8e14 kJ of energy in two hours. This does not account for decreased light in the penumbral shadow, but geometry will not allow that decrease to be more than double, so we can use 9.6e14 kJ as our upper bound. Thus, with a maximum of five solar eclipses per year, the greatest possible decrease in energy incident on the earth due to eclipses is 4.8e18 J.

How does this measure up? Well, approximately 5.5e24 J of solar energy strikes the earth every year. So, at most, solar eclipses block 0.000087% of the energy the Earth receives per year from the sun. Probably not going to be enough to make a difference.

FredTheRanger wrote:Would someone please explain to me why, in Figure 3, he seems to be saying that the Moon repels the Earth?

He's not saying that the Moon repels the Earth. That figure is showing how the Earth and Moon both orbit around their mutual center of gravity, and that point in between them is in turn the point that follows an elliptical path around the sun. The combined effect of the Earth-Moon orbit and the (Earth-Moon)-Sun orbit is that the Earth's path around the sun is not a perfect ellipse, but wobbles closer and further from the sun on a monthly cycle, as the Earth is sometimes on the sunward side of the center of gravity between it and the moon, and sometimes opposite that, on the spaceward side.

sevenperforce wrote:Typically, the totality track of the moon's shadow during an eclipse is approximately 250 km wide. The maximum duration of an eclipse is a little over two hours. While totality does not exist for this entire duration, we will pretend it does for the purposes of establishing an upper bound.

With the above values, each eclipse blocks a 4.9e10 m2 of area for two hours. Solar insolation at the top of the atmosphere is 1.37 kW/m2, so each eclipse blocks a total of 4.8e14 kJ of energy in two hours. This does not account for decreased light in the penumbral shadow, but geometry will not allow that decrease to be more than double, so we can use 9.6e14 kJ as our upper bound.

The penumbral shadow is severals thousend km wide and causes almost all the energy loss. Much more than double. As you can see in cases where is no total eclipse, for example an annular eclipse.A more detailed calculation shows that my initial guess was too high.With 6 to 7 hours per year solar eclipses which block about (r_moon/r_earth)^2 of the sunlight it should be 0.005% to 0.006% of the sunlight.

sevenperforce wrote:Each eclipse blocks a 4.9e10 m2 of area for two hours. Solar insolation at the top of the atmosphere is 1.37 kW/m2, so each eclipse blocks a total of 4.8e14 kJ of energy in two hours. This does not account for decreased light in the penumbral shadow, but geometry will not allow that decrease to be more than double, so we can use 9.6e14 kJ as our upper bound.

The penumbral shadow is severals thousend km wide and causes almost all the energy loss. Much more than double.

Well, the penumbral shadow is definitely quite wide, but why would it be responsible for the majority of the energy loss? I haven't worked out the geometry exactly, but it would seem that the percentage of the sun's disc obscured by the moon would drop off very rapidly as you moved away from the region of totality...1/r if not 1/r2. I guess you'd have to work out the integral to know exactly.

I want to know how the change in size would have affected asteroids that formerly would have hit the moon? I know the moon protects us from many hits. What would happen if an asteroid were to contact the moon black hole?

Overload_ed wrote:I want to know how the change in size would have affected asteroids that formerly would have hit the moon? I know the moon protects us from many hits. What would happen if an asteroid were to contact the moon black hole?

It depends on the size of the asteroid. Smaller asteroids passing close to the black hole moon will be torn apart by tidal forces and form a ring, then an accretion disk. The larger the asteroid, the closer it will have to come to the event horizon to be torn apart; otherwise it will be flung off in another direction. Assuming that asteroids can approach from any direction, this neither increases or decreases the chance of it hitting the Earth.

However, since the distance at which tidal forces would rip an asteroid apart is much lower than the current radius of the moon, most trajectories which would have formerly impacted the lunar surface would instead pass by, thus having a greater chance of hitting Earth.